Finite Group Databasebeta

← #16031097

Subgroups — #16031097

Order 3328.

2992 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719262C211yesmaximal, characteristic, complemented
2#13119076C212yesmaximal, complemented
3#13118896C212yesmaximal, complemented
4#13118737C212yesmaximal, complemented
5#13118702C211yesmaximal, characteristic, complemented
6#13118617C211yesmaximal, characteristic, complemented
7#13118554C211yesmaximal, characteristic, complemented
8#13118483C211yesmaximal, characteristic, complemented
9#13118407C211yesmaximal, characteristic, complemented
10#13118322C211yesmaximal, characteristic, complemented
11#13118298C212yesmaximal, complemented
12#13118281C211yesmaximal, characteristic, complemented
13#13118186C211yesmaximal, characteristic
14#13118095C212yesmaximal, complemented
15#13118078C212yesmaximal, complemented
16C4×#88190C211yesmaximal, characteristic, complemented
17C4×#88178C211yesmaximal, characteristic, complemented
18C4×#88192C211yesmaximal, characteristic, complemented
19C4×#88207C212yesmaximal, complemented
20#13117301C211yesmaximal, characteristic, complemented
21#13117219C212yesmaximal, complemented
22C42×C22⋊D13C211yesmaximal, characteristic, complemented
23C22×C4×D4×C13C211yesmaximal, characteristic, complemented
24C23×D4×C13C2211yescharacteristic
25C24×C4×C13C2212yes—
26C2×C4×D4×C13—28no—
27C2×C4×D4×C13C2212yes—
28C2×C4×D4×C13C2211yescharacteristic
29C2×C4×D4×C13C2212yes—
30C2×C4×D4×C13C2211yescharacteristic
31C2×C4×D4×C13C2211yescharacteristic
32C2×C4×D4×C13C2211yescharacteristic
33C22×C13×C4⋊C4C2211yescharacteristic
34C22×C13×C22⋊C4C2212yes—
35C22×C42×C13C2211yescharacteristic
36C2×#88207C2212yes—
37C2×#88192C2211yescharacteristic
38C2×#88192C2211yescharacteristic
39C2×#88190C2211yescharacteristic
40C2×#88190C2211yescharacteristic
41C2×C4×C22⋊D13C2211yescharacteristic
42C2×C4×C22⋊D13C2211yescharacteristic
43C2×C4×C22⋊D13C2211yescharacteristic
44C2×C4×C22⋊D13C2212yescomplemented
45C2×C4×C22⋊D13C2212yescomplemented
46C2×#88180C2212yescomplemented
47C2×#88180C2212yescomplemented
48C2×#88178C2211yescharacteristic
49#11719262—28no—
50C2×#88151C2211yescharacteristic, complemented
51C2×#88144C2211yescharacteristic, complemented
52C2×#88137C2212yescomplemented
53C2×#88133C2212yescomplemented
54C2×C42×D13C2211yescharacteristic, complemented
55C2×C4×Dic26C2211yescharacteristic, complemented
56#11718908C2212yes—
57#11718908C2212yes—
58#11718908C2212yes—
59#11718884C2212yes—
60#11718883C2212yes—
61#11718883C2212yes—
62#11718883C2212yes—
63#11718882C2211yescharacteristic
64#11718882C2211yescharacteristic
65#11718882C2211yescharacteristic
66#11718882C2211yescharacteristic
67#11718874C2212yes—
68#11718874C2212yescomplemented
69#11718874C2212yescomplemented
70#11718873C2212yes—
71#11718873C2212yes—
72#11718873C2211yescharacteristic
73#11718873C2212yescomplemented
74#11718873C2212yescomplemented
75#11718872C2212yescomplemented
76#11718872C2212yescomplemented
77#11718871C2212yes—
78#11718871C2212yes—
79#11718871C2212yescomplemented
80#11718871C2212yescomplemented
81C4×C22⋊Dic13C2211yescharacteristic
82C4×C22⋊Dic13C2211yescharacteristic
83C4×C22⋊Dic13C2212yes—
84C4×C22⋊Dic13C2211yescharacteristic
85C4×C22⋊Dic13C2212yescomplemented
86C4×C22⋊Dic13C2212yescomplemented
87C4×C22⋊Dic13C2212yescomplemented
88C4×C22⋊Dic13C2212yescomplemented
89#11718655C2212yescomplemented
90#11718648C2211yescharacteristic, complemented
91#11718647C2212yescomplemented
92#11718646C2211yescharacteristic, complemented
93#11718646C2211yescharacteristic, complemented
94#11718645C2212yescomplemented
95#11718644C2212yescomplemented
96#11718638C2211yescharacteristic, complemented
97#11718635C2211yescharacteristic, complemented
98#11718634C2211yescharacteristic, complemented
99#11718622C2212yescomplemented
100#11718620C2212yescomplemented
101#11718617C2212yescomplemented
102#11718614C2212yescomplemented
103#11718613C2212yescomplemented
104#11718613C2212yescomplemented
105#11718613C2212yescomplemented
106#11718612C2212yescomplemented
107#11718612C2212yescomplemented
108#11718610C2212yescomplemented
109#11718609C2212yescomplemented
110#11718606C2212yescomplemented
111#11718606C2212yescomplemented
112#11718605C2212yescomplemented
113C4×#6103C2211yescharacteristic, complemented
114C4×#6103C2211yescharacteristic, complemented
115C4×#6103C2211yescharacteristic, complemented
116C4×C4⋊Dic13C2211yescharacteristic, complemented
117#11718594C2212yescomplemented
118C4×#6101C2212yescomplemented
119C4×#6101C2211yescharacteristic, complemented
120C4×#6101C2211yescharacteristic, complemented
121C4×#6101C2211yescharacteristic, complemented
122C42×Dic13C2211yescharacteristic, complemented
123#11718590C2211yescharacteristic, complemented
124#11718589C2211yescharacteristic, complemented
125C25×C13C2312yes—
126C22×D4×C13—24no—
127C22×D4×C13—24no—
128C22×D4×C13—24no—
129C22×D4×C13C2312yes—
130C22×D4×C13C2311yescharacteristic
131C22×D4×C13C2311yescharacteristic
132C23×C4×C13—28no—
133C23×C4×C13—28no—
134C23×C4×C13—44no—
135C23×C4×C13C2312yes—
136C23×C4×C13C2311yescharacteristic
137C23×C4×C13C2312yes—
138C23×C4×C13C2312yes—
139C23×C4×C13C2312yes—
140C23×C4×C13C2312yes—
141C23×C4×C13C2311yescharacteristic
142C23×C4×C13C2311yescharacteristic
143C22×C22⋊D13C2312yes—
144C22×C22⋊D13C2312yes—
145C22×C22⋊D13C2311yescharacteristic
146C22×C4×D13C2311yescharacteristic
147C22×C4×D13C2311yescharacteristic
148C22×C4×D13C2311yescharacteristic
149C22×Dic26C2311yescharacteristic
150C4×D4×C13—24no—
151C4×D4×C13—28no—
152C4×D4×C13—24no—
153C4×D4×C13—28no—
154C4×D4×C13—24no—
155C4×D4×C13D418yescomplemented
156C2×C13×C4⋊C4—24no—
157C2×C13×C4⋊C4C2311yescharacteristic
158C2×C13×C4⋊C4C2312yes—
159C2×C13×C4⋊C4C2311yescharacteristic
160C2×C13×C22⋊C4—28no—
161C2×C13×C22⋊C4C2312yes—
162C2×C13×C22⋊C4C2312yes—
163C2×C13×C22⋊C4C2312yes—
164C2×C13×C22⋊C4C2312yes—
165C2×C42×C13—24no—
166C2×C42×C13C2311yescharacteristic
167C2×C42×C13C2311yescharacteristic
168C2×C42×C13C2311yescharacteristic
169C2×C42×C13C2311yescharacteristic
170#88207—28no—
171C2×C22⋊Dic13C2312yes—
172C2×C22⋊Dic13C2312yes—
173C2×C22⋊Dic13C2312yes—
174C2×C22⋊Dic13C2312yes—
175C2×C22⋊Dic13C2311yescharacteristic
176C2×C22⋊Dic13C2311yescharacteristic
177C2×C22⋊Dic13C2311yescharacteristic
178C2×C22⋊Dic13C2312yes—
179C2×C22⋊Dic13C2312yes—
180C2×C22⋊Dic13C2312yes—
181C2×C22⋊Dic13C2312yes—
182C2×C22⋊Dic13C2312yes—
183C2×C22⋊Dic13C2312yes—
184C2×C22⋊Dic13C2312yes—
185C2×C22⋊Dic13C2312yes—
186C2×C22⋊Dic13C2312yes—
187C2×C22⋊Dic13C2312yes—
188C2×C22⋊Dic13C2312yes—
189C2×C22⋊Dic13C2312yes—
190#88192—24no—
191#88192—24no—
192#88190—24no—
193#88190—24no—
194C4×C22⋊D13—28no—
195C4×C22⋊D13—24no—
196C4×C22⋊D13—24no—
197C4×C22⋊D13—24no—
198C4×C22⋊D13—44no—
199C2×#6103C2312yes—
200C2×#6103C2311yescharacteristic
201C2×#6103C2311yescharacteristic
202C2×#6103C2311yescharacteristic
203C2×#6103C2312yes—
204#88180—28no—
205#88180—44no—
206C2×C4⋊Dic13C2311yescharacteristic
207C2×C4⋊Dic13C2312yes—
208C2×C4⋊Dic13C2312yes—
209C2×C4⋊Dic13C2311yescharacteristic
210C2×C4⋊Dic13C2311yescharacteristic
211C2×C4⋊Dic13C2312yes—
212C2×C4⋊Dic13C2312yes—
213#88178—24no—
214C2×#6101C2312yes—
215C2×#6101C2312yes—
216C2×#6101C2312yes—
217C2×#6101C2311yescharacteristic
218C2×#6101C2311yescharacteristic
219C2×#6101C2311yescharacteristic
220C2×#6101C2312yes—
221C2×#6101C2312yes—
222C2×C4×Dic13C2312yes—
223C2×C4×Dic13C2311yescharacteristic
224C2×C4×Dic13C2311yescharacteristic
225C2×C4×Dic13C2311yescharacteristic
226C2×C4×Dic13C2311yescharacteristic
227C2×C4×Dic13C2312yes—
228C2×C4×Dic13C2311yescharacteristic
229C2×C4×Dic13C2311yescharacteristic
230C2×C4×Dic13C2311yescharacteristic
231C2×C4×Dic13C2311yescharacteristic
232C2×C4×Dic13C2311yescharacteristic
233#88151—24no—
234#88144—24no—
235#88137—28no—
236#88133—28no—
237C42×D13—24no—
238C4×Dic26—24no—
239#88071C2312yes—
240#88071C2312yes—
241#88071C2312yes—
242#88071C2312yes—
243#88071C2311yescharacteristic
244#88071C2311yescharacteristic
245#88071C2311yescharacteristic
246#88071C2311yescharacteristic
247#88071C2311yescharacteristic
248#88071C2311yescharacteristic
249#88071C2312yes—
250#88071C2312yes—
251#88071C2312yes—
252#88071C2312yes—
253#88071C2312yes—
254#88071C2312yes—
255#88071C2312yes—
256#88071C2312yes—
257#88071C2312yes—
258#34700—131nomaximal, Sylow
259C24×C13—24no—
260C24×C13—24no—
261C24×C13—24no—
262C24×C13—24no—
263C24×C13—24no—
264C24×C13—42no—
265C24×C13—42no—
266C24×C13C2412yes—
267C24×C13C2412yes—
268C24×C13C2411yescharacteristic
269C23×D13C2411yescharacteristic
270C2×D4×C13—232no—
271C2×D4×C13—24no—
272C2×D4×C13—24no—
273C2×D4×C13—22no—
274C2×D4×C13—24no—
275C2×D4×C13—22no—
276C2×D4×C13—22no—
277C2×D4×C13—22no—
278C2×D4×C13C2×D414yes—
279C2×D4×C13#4114yes—
280C22×C4×C13—22no—
281C22×C4×C13—22no—
282C22×C4×C13—24no—
283C22×C4×C13—22no—
284C22×C4×C13—24no—
285C22×C4×C13—22no—
286C22×C4×C13—24no—
287C22×C4×C13—22no—
288C22×C4×C13—24no—
289C22×C4×C13—22no—
290C22×C4×C13—24no—
291C22×C4×C13—24no—
292C22×C4×C13—24no—
293C22×C4×C13—24no—
294C22×C4×C13—24no—
295C22×C4×C13—24no—
296C22×C4×C13—24no—
297C22×C4×C13—42no—
298C22×C4×C13—42no—
299C22×C4×C13—42no—
300C22×C4×C13—41no—
301C22×C4×C13—432no—
302C22×C4×C13C2×D418yes—
303C22×C4×C13#4114yes—
304C22×C4×C13#4114yes—
305C22×C4×C13C2412yes—
306C22×C4×C13C2411yescharacteristic
307C22×C4×C13C2411yescharacteristic
308C22×C4×C13C2412yes—
309C22×C4×C13C2411yescharacteristic
310C22×C4×C13C2411yescharacteristic
311C22×C4×C13C2411yescharacteristic
312C22×C4×C13C2411yescharacteristic
313C2×C22⋊D13—22no—
314C2×C22⋊D13—22no—
315C2×C22⋊D13—24no—
316C2×C22⋊D13—24no—
317C2×C22⋊D13—24no—
318C2×C22⋊D13—24no—
319C2×C22⋊D13—42no—
320C2×C22⋊D13—42no—
321C2×C22⋊D13#4114yes—
322C22×Dic13C2411yescharacteristic
323C22×Dic13C2412yes—
324C22×Dic13C2411yescharacteristic
325C22×Dic13C2411yescharacteristic
326C22×Dic13C2411yescharacteristic
327C22×Dic13C2411yescharacteristic
328C22×Dic13C2412yes—
329C22×Dic13C2412yes—
330C22×Dic13C2412yes—
331C22×Dic13C2411yescharacteristic
332C22×Dic13C2411yescharacteristic
333C2×C4×D13—22no—
334C2×C4×D13—22no—
335C2×C4×D13—22no—
336C2×C4×D13—22no—
337C2×C4×D13—22no—
338C2×C4×D13—22no—
339C2×C4×D13—22no—
340C2×C4×D13—22no—
341C2×C4×D13—41no—
342C2×Dic26—22no—
343C2×Dic26—22no—
344C2×Dic26—22no—
345C13×C4⋊C4—24no—
346C13×C4⋊C4—22no—
347C13×C4⋊C4C2×D414yes—
348C13×C22⋊C4—24no—
349C13×C22⋊C4—24no—
350C13×C22⋊C4—24no—
351C13×C22⋊C4C2×D418yes—
352C42×C13—22no—
353C42×C13—22no—
354C42×C13—22no—
355C42×C13C2×D414yes—
356C22⋊Dic13—24no—
357C22⋊Dic13—24no—
358C22⋊Dic13—24no—
359C22⋊Dic13—24no—
360C22⋊Dic13—22no—
361C22⋊Dic13—22no—
362C22⋊Dic13—22no—
363C22⋊Dic13—24no—
364C22⋊Dic13—24no—
365C22⋊Dic13—24no—
366C22⋊Dic13—24no—
367C22⋊Dic13—24no—
368C22⋊Dic13—24no—
369C22⋊Dic13—42no—
370C22⋊Dic13—42no—
371C22⋊Dic13—42no—
372C22⋊Dic13—42no—
373C22⋊Dic13—42no—
374C22⋊Dic13—42no—
375#6103—22no—
376#6103—24no—
377#6103—22no—
378#6103—22no—
379#6103—42no—
380C4⋊Dic13—22no—
381C4⋊Dic13—24no—
382C4⋊Dic13—24no—
383C4⋊Dic13—22no—
384C4⋊Dic13—22no—
385C4⋊Dic13—42no—
386C4⋊Dic13—42no—
387#6101—24no—
388#6101—24no—
389#6101—24no—
390#6101—22no—
391#6101—22no—
392#6101—22no—
393#6101—42no—
394#6101—42no—
395C4×Dic13—24no—
396C4×Dic13—22no—
397C4×Dic13—22no—
398C4×Dic13—22no—
399C4×Dic13—22no—
400C4×Dic13—22no—
401C4×Dic13—22no—
402C4×Dic13—22no—
403C4×Dic13—24no—
404C4×Dic13—22no—
405C4×Dic13—41no—
406C2×#529—131no—
407C22×C4×D4D1311yescharacteristic, complemented
408#2480—132no—
409#2468—132no—
410#2457—132no—
411#2454—131no—
412#2447—131no—
413#2442—131no—
414#2435—131no—
415#2427—131no—
416#2420—131no—
417#2418—132no—
418#2417—131no—
419#2408—131no—
420#2395—132no—
421#2392—132no—
422C4×#124—131no—
423C4×C22⋊Q8—131no—
424C4×#121—131no—
425C4×#120—132no—
426#2293—131no—
427#2280—132no—
428C42×D4—131no—
429C23×C13—21no—
430C23×C13—21no—
431C23×C13—21no—
432C23×C13—21no—
433C23×C13—216no—
434C23×C13—22no—
435C23×C13—22no—
436C23×C13—22no—
437C23×C13—22no—
438C23×C13—22no—
439C23×C13—22no—
440C23×C13—22no—
441C23×C13—22no—
442C23×C13—22no—
443C23×C13—22no—
444C23×C13—22no—
445C23×C13—22no—
446C23×C13—48no—
447C23×C13—48no—
448C23×C13—48no—
449C23×C13—48no—
450C23×C13—48no—
451C23×C13—48no—
452C23×C13C22×D414yes—
453C23×C13C2×#4114yes—
454C23×C13C2×#4112yes—
455C23×C13C2×#4112yes—
456C23×C13C2×#4112yes—
457C23×C13C2511yescharacteristic
458C22×D13—21no—
459C22×D13—21no—
460C22×D13—21no—
461C22×D13—21no—
462C22×D13—21no—
463C22×D13—21no—
464C22×D13C2×#4112yes—
465D4×C13—216no—
466D4×C13—28no—
467D4×C13—28no—
468C2×C4×C13—21no—
469C2×C4×C13—21no—
470C2×C4×C13—21no—
471C2×C4×C13—22no—
472C2×C4×C13—21no—
473C2×C4×C13—22no—
474C2×C4×C13—21no—
475C2×C4×C13—21no—
476C2×C4×C13—28no—
477C2×C4×C13—28no—
478C2×C4×C13—216no—
479C2×C4×C13—21no—
480C2×C4×C13—22no—
481C2×C4×C13—21no—
482C2×C4×C13—22no—
483C2×C4×C13—22no—
484C2×C4×C13—21no—
485C2×C4×C13—48no—
486C2×C4×C13—44no—
487C2×C4×C13—48no—
488C2×C4×C13—48no—
489C2×C4×C13—48no—
490C2×C4×C13C22×D412yes—
491C2×C4×C13C22×D414yes—
492C2×C4×C13C22×D412yes—
493C2×C4×C13C22×D412yes—
494C2×C4×C13C2×#4112yes—
495C2×C4×C13C2×#4112yes—
496C2×C4×C13C2×#4112yes—
497C2×C4×C13C2×#4112yes—
498C2×C4×C13C2×#4112yes—
499C2×C4×C13H(5,𝔽2)12yes—
500C22⋊D13—28no—
501C22⋊D13—48no—
502C22⋊D13—48no—
503C2×Dic13—21no—
504C2×Dic13—21no—
505C2×Dic13—21no—
506C2×Dic13—21no—
507C2×Dic13—21no—
508C2×Dic13—22no—
509C2×Dic13—22no—
510C2×Dic13—21no—
511C2×Dic13—21no—
512C2×Dic13—21no—
513C2×Dic13—21no—
514C2×Dic13—21no—
515C2×Dic13—22no—
516C2×Dic13—22no—
517C2×Dic13—21no—
518C2×Dic13—21no—
519C2×Dic13—21no—
520C2×Dic13—22no—
521C2×Dic13—22no—
522C2×Dic13—21no—
523C2×Dic13—22no—
524C2×Dic13—22no—
525C2×Dic13—22no—
526C2×Dic13—21no—
527C2×Dic13—21no—
528C2×Dic13—22no—
529C2×Dic13—21no—
530C2×Dic13—21no—
531C2×Dic13—21no—
532C2×Dic13—22no—
533C2×Dic13—22no—
534C2×Dic13—21no—
535C2×Dic13C2×#4112yes—
536C4×D13—44no—
537C4×D13—44no—
538C4×D13—44no—
539Dic26—44no—
540C23×D4C2×D1311yescharacteristic
541C24×C4C2×D1312yes—
542#529—268no—
543C2×#126—132no—
544C2×#125—131no—
545C2×#124—131no—
546C2×#124—131no—
547C2×#123—132no—
548C2×C22⋊Q8—131no—
549C2×C22⋊Q8—131no—
550C2×#121—131no—
551C2×#121—131no—
552C2×#120—132no—
553C2×C4×Q8—131no—
554C2×C4×D4—28no—
555C2×C4×D4—131no—
556C2×C4×D4—131no—
557C2×C4×D4—131no—
558C2×C4×D4—132no—
559C2×C4×D4—132no—
560C2×C4×D4C2×D1312yes—
561C2×C4×D4C2×D1311yescharacteristic
562C2×C4×D4C2×D1311yescharacteristic
563C2×C4×D4C2×D1312yes—
564C2×C4×D4C2×D1311yescharacteristic
565C2×C4×D4C2×D1311yescharacteristic
566C2×#117—132no—
567C2×#117—132no—
568C22×C4⋊C4C2×D1311yescharacteristic
569C22×C22⋊C4C2×D1312yes—
570C22×C42—131no—
571C22×C42C2×D1311yescharacteristic
572#400—132no—
573#399—132no—
574#398—132no—
575#398—132no—
576#397—132no—
577#397—132no—
578#397—132no—
579#397—132no—
580#396—132no—
581#396—132no—
582#394—132no—
583#394—132no—
584#394—132no—
585#394—132no—
586#394—132no—
587#392—132no—
588#391—131no—
589#391—131no—
590#390—131no—
591#390—131no—
592#390—131no—
593#390—131no—
594#389—131no—
595#389—131no—
596#389—131no—
597#389—131no—
598#388—132no—
599#388—132no—
600#388—132no—
601#388—132no—
602#388—132no—
603#387—132no—
604#386—132no—
605#386—132no—
606#386—132no—
607#386—132no—
608#385—132no—
609#385—132no—
610#385—132no—
611#385—132no—
612#382—131no—
613#381—132no—
614#381—132no—
615#380—131no—
616#380—132no—
617#380—132no—
618#380—132no—
619#380—132no—
620#380—131no—
621#379—132no—
622#379—132no—
623#379—132no—
624C4×C4⋊C4—132no—
625C4×C4⋊C4—131no—
626C4×C4⋊C4—131no—
627C4×C4⋊C4—131no—
628C4×C4⋊C4—131no—
629C4×C22⋊C4—132no—
630C4×C22⋊C4—132no—
631C4×C22⋊C4—132no—
632C4×C22⋊C4—132no—
633C4×C22⋊C4—131no—
634C4×C22⋊C4—131no—
635C4×C22⋊C4—131no—
636C4×C22⋊C4—132no—
637C4×C22⋊C4—131no—
638C4×C22⋊C4—131no—
639C4×C22⋊C4—131no—
640C43—131no—
641C22×C13—22no—
642C22×C13—22no—
643C22×C13—22no—
644C22×C13—22no—
645C22×C13—22no—
646C22×C13—22no—
647C22×C13—24no—
648C22×C13—24no—
649C22×C13—24no—
650C22×C13—24no—
651C22×C13—24no—
652C22×C13—24no—
653C22×C13—432no—
654C22×C13—42no—
655C22×C13—42no—
656C22×C13—42no—
657C22×C13—42no—
658C22×C13—42no—
659C22×C13—42no—
660C22×C13—42no—
661C22×C13—42no—
662C22×C13#52914yescomplemented
663C22×C13C23×D411yescharacteristic
664C22×C13C22×#4111yescharacteristic
665C22×C13C22×#4111yescharacteristic
666C22×C13C22×#4111yescharacteristic
667C22×C13C22×#4111yescharacteristic
668C22×C13C2×H(5,𝔽2)11yescharacteristic
669C22×C13#58511yescharacteristic
670C2×D13—22no—
671C2×D13—22no—
672C2×D13—22no—
673C2×D13—41no—
674C2×D13—41no—
675C2×D13—41no—
676C2×D13—41no—
677C4×C13—22no—
678C4×C13—22no—
679C4×C13—24no—
680C4×C13—22no—
681C4×C13—42no—
682C4×C13—41no—
683C4×C13#52514yes—
684C4×C13#54614yes—
685Dic13—22no—
686Dic13—42no—
687Dic13—41no—
688Dic13—41no—
689Dic13—42no—
690Dic13—41no—
691Dic13—41no—
692Dic13—42no—
693Dic13—41no—
694Dic13—41no—
695Dic13—42no—
696C25C22×D1312yes—
697C22×Q8—131no—
698C22×D4—24no—
699C22×D4—24no—
700C22×D4—24no—
701C22×D4—131no—
702C22×D4—132no—
703C22×D4—132no—
704C22×D4C22×D1312yes—
705C22×D4C22×D1311yescharacteristic
706C22×D4C22×D1311yescharacteristic
707C23×C4—28no—
708C23×C4—28no—
709C23×C4—44no—
710C23×C4—131no—
711C23×C4—131no—
712C23×C4—131no—
713C23×C4C22×D1312yes—
714C23×C4C22×D1311yescharacteristic
715C23×C4C22×D1312yes—
716C23×C4C22×D1312yes—
717C23×C4C22×D1312yes—
718C23×C4C22×D1311yescharacteristic
719C23×C4C22×D1311yescharacteristic
720C23×C4C22×D1312yes—
721#126—268no—
722#125—264no—
723#124—264no—
724#124—264no—
725#123—268no—
726C22⋊Q8—264no—
727C22⋊Q8—264no—
728#121—264no—
729#121—264no—
730#120—268no—
731C4×Q8—264no—
732C4×D4—24no—
733C4×D4—28no—
734C4×D4—24no—
735C4×D4—28no—
736C4×D4—24no—
737C4×D4—264no—
738C4×D4—264no—
739C4×D4—264no—
740C4×D4—268no—
741C4×D4—524no—
742C4×D4C22⋊D1318yescomplemented
743#117—268no—
744#117—524no—
745C2×C4⋊C4—24no—
746C2×C4⋊C4—132no—
747C2×C4⋊C4—132no—
748C2×C4⋊C4—132no—
749C2×C4⋊C4—131no—
750C2×C4⋊C4—131no—
751C2×C4⋊C4—131no—
752C2×C4⋊C4—131no—
753C2×C4⋊C4—132no—
754C2×C4⋊C4—131no—
755C2×C4⋊C4—132no—
756C2×C4⋊C4—131no—
757C2×C4⋊C4—132no—
758C2×C4⋊C4—132no—
759C2×C4⋊C4—132no—
760C2×C4⋊C4—132no—
761C2×C4⋊C4C22×D1311yescharacteristic
762C2×C4⋊C4C22×D1312yes—
763C2×C4⋊C4C22×D1311yescharacteristic
764C2×C22⋊C4—28no—
765C2×C22⋊C4—132no—
766C2×C22⋊C4—132no—
767C2×C22⋊C4—132no—
768C2×C22⋊C4—131no—
769C2×C22⋊C4—131no—
770C2×C22⋊C4—131no—
771C2×C22⋊C4—132no—
772C2×C22⋊C4—132no—
773C2×C22⋊C4—132no—
774C2×C22⋊C4—132no—
775C2×C22⋊C4—132no—
776C2×C22⋊C4—132no—
777C2×C22⋊C4—132no—
778C2×C22⋊C4—132no—
779C2×C22⋊C4—131no—
780C2×C22⋊C4—131no—
781C2×C22⋊C4—131no—
782C2×C22⋊C4—132no—
783C2×C22⋊C4—132no—
784C2×C22⋊C4—132no—
785C2×C22⋊C4—132no—
786C2×C22⋊C4—132no—
787C2×C22⋊C4—132no—
788C2×C22⋊C4—132no—
789C2×C22⋊C4C22×D1312yes—
790C2×C22⋊C4C22×D1312yes—
791C2×C22⋊C4C22×D1312yes—
792C2×C22⋊C4C22×D1312yes—
793C2×C42—24no—
794C2×C42—131no—
795C2×C42—131no—
796C2×C42—131no—
797C2×C42—131no—
798C2×C42—131no—
799C2×C42—131no—
800C2×C42—131no—
801C2×C42—132no—
802C2×C42—132no—
803C2×C42—131no—
804C2×C42—131no—
805C2×C42—264no—
806C2×C42C22×D1311yescharacteristic
807C2×C42C22×D1311yescharacteristic
808C2×C42C22×D1311yescharacteristic
809C2×C42C22×D1311yescharacteristic
810#95—131no—
811#95—131no—
812#95—131no—
813#95—131no—
814#95—131no—
815#95—131no—
816#95—132no—
817#95—132no—
818#95—132no—
819#95—132no—
820#95—132no—
821#95—132no—
822#95—132no—
823#95—132no—
824#95—132no—
825#95—132no—
826#95—132no—
827#95—132no—
828#95—132no—
829C2×C13—24no—
830C2×C13—44no—
831C2×C13—44no—
832C2×C13C2×#52511yescharacteristic
833C2×C13C2×#52911yescharacteristic
834C2×C13#346011yescharacteristic
835C2×C13C2×#54611yescharacteristic
836C2×C13D4×#4111yescharacteristic
837C2×C13#347511yescharacteristic
838C2×C13#348111yescharacteristic
839D13—42no—
840C24—24no—
841C24—24no—
842C24—24no—
843C24—24no—
844C24—24no—
845C24—42no—
846C24—42no—
847C24—131no—
848C24C23×D1312yes—
849C24C23×D1312yes—
850C24C23×D1311yescharacteristic
851C2×Q8—262no—
852C2×Q8—262no—
853C2×Q8—262no—
854C2×D4—232no—
855C2×D4—24no—
856C2×D4—24no—
857C2×D4—24no—
858C2×D4—22no—
859C2×D4—22no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—134no—
863C2×D4—262no—
864C2×D4—262no—
865C2×D4—264no—
866C2×D4—264no—
867C2×D4—264no—
868C2×D4—264no—
869C2×D4—522no—
870C2×D4—522no—
871C2×D4#612714yes—
872C2×D4C2×C22⋊D1314yes—
873C22×C4—22no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—24no—
880C22×C4—22no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—22no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—41no—
894C22×C4—432no—
895C22×C4—131no—
896C22×C4—131no—
897C22×C4—132no—
898C22×C4—131no—
899C22×C4—131no—
900C22×C4—131no—
901C22×C4—131no—
902C22×C4—132no—
903C22×C4—132no—
904C22×C4—132no—
905C22×C4—131no—
906C22×C4—262no—
907C22×C4—262no—
908C22×C4—262no—
909C22×C4—262no—
910C22×C4—262no—
911C22×C4—262no—
912C22×C4—262no—
913C22×C4—262no—
914C22×C4—521no—
915C22×C4#612714yes—
916C22×C4#612914yes—
917C22×C4C2×C22⋊D1318yes—
918C22×C4C23×D1312yes—
919C22×C4C23×D1311yescharacteristic
920C22×C4C23×D1311yescharacteristic
921C22×C4C23×D1311yescharacteristic
922C22×C4C23×D1311yescharacteristic
923C22×C4C23×D1312yes—
924C22×C4C23×D1311yescharacteristic
925C22×C4C23×D1311yescharacteristic
926C4⋊C4—24no—
927C4⋊C4—22no—
928C4⋊C4—262no—
929C4⋊C4—262no—
930C4⋊C4—262no—
931C4⋊C4—264no—
932C4⋊C4—262no—
933C4⋊C4—262no—
934C4⋊C4—264no—
935C4⋊C4—264no—
936C4⋊C4—264no—
937C4⋊C4—262no—
938C4⋊C4—264no—
939C4⋊C4—522no—
940C4⋊C4—522no—
941C4⋊C4—522no—
942C4⋊C4—522no—
943C4⋊C4C2×C22⋊D1314yes—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—262no—
948C22⋊C4—264no—
949C22⋊C4—264no—
950C22⋊C4—262no—
951C22⋊C4—264no—
952C22⋊C4—264no—
953C22⋊C4—264no—
954C22⋊C4—264no—
955C22⋊C4—262no—
956C22⋊C4—262no—
957C22⋊C4—264no—
958C22⋊C4—264no—
959C22⋊C4—264no—
960C22⋊C4—264no—
961C22⋊C4—262no—
962C22⋊C4—262no—
963C22⋊C4—264no—
964C22⋊C4—522no—
965C22⋊C4—522no—
966C22⋊C4—522no—
967C22⋊C4—522no—
968C22⋊C4—522no—
969C22⋊C4—522no—
970C22⋊C4—522no—
971C22⋊C4C2×C22⋊D1318yes—
972C42—22no—
973C42—22no—
974C42—22no—
975C42—262no—
976C42—262no—
977C42—262no—
978C42—262no—
979C42—262no—
980C42—264no—
981C42—262no—
982C42—262no—
983C42—262no—
984C42—264no—
985C42—521no—
986C42C2×C22⋊D1314yes—
987C13#3470011yescharacteristic, complemented, Sylow
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—216no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—48no—
1006C23—48no—
1007C23—48no—
1008C23—48no—
1009C23—48no—
1010C23—48no—
1011C23—132no—
1012C23—261no—
1013C23—261no—
1014C23—261no—
1015C23—261no—
1016C23—261no—
1017C23—261no—
1018C23C2×#612714yes—
1019C23C2×#612712yes—
1020C23C2×#612912yes—
1021C23#41×D1312yes—
1022C23C22×C22⋊D1314yes—
1023C23C24×D1311yescharacteristic
1024Q8—524no—
1025D4—216no—
1026D4—28no—
1027D4—28no—
1028D4—268no—
1029D4—528no—
1030D4—528no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—28no—
1040C2×C4—28no—
1041C2×C4—216no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—48no—
1049C2×C4—48no—
1050C2×C4—48no—
1051C2×C4—44no—
1052C2×C4—48no—
1053C2×C4—132no—
1054C2×C4—261no—
1055C2×C4—261no—
1056C2×C4—261no—
1057C2×C4—261no—
1058C2×C4—261no—
1059C2×C4—261no—
1060C2×C4—262no—
1061C2×C4—262no—
1062C2×C4—261no—
1063C2×C4—262no—
1064C2×C4—262no—
1065C2×C4—261no—
1066C2×C4—261no—
1067C2×C4—262no—
1068C2×C4—261no—
1069C2×C4—261no—
1070C2×C4—262no—
1071C2×C4—261no—
1072C2×C4—261no—
1073C2×C4—262no—
1074C2×C4—262no—
1075C2×C4—261no—
1076C2×C4—261no—
1077C2×C4—261no—
1078C2×C4—262no—
1079C2×C4—261no—
1080C2×C4—262no—
1081C2×C4—261no—
1082C2×C4—261no—
1083C2×C4—261no—
1084C2×C4—262no—
1085C2×C4—262no—
1086C2×C4—524no—
1087C2×C4—524no—
1088C2×C4—524no—
1089C2×C4C2×#612712yes—
1090C2×C4C2×#612712yes—
1091C2×C4C2×#612712yes—
1092C2×C4C2×#612912yes—
1093C2×C4C2×#612912yes—
1094C2×C4#8825112yes—
1095C2×C4C22×C22⋊D1312yes—
1096C2×C4C22×C22⋊D1314yes—
1097C2×C4C22×C22⋊D1312yes—
1098C2×C4C22×C22⋊D1312yes—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—22no—
1104C22—22no—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—432no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—262no—
1121C22—262no—
1122C22—262no—
1123C22—521no—
1124C22—521no—
1125C22—521no—
1126C22—521no—
1127C22#1171926214yescomplemented
1128C22C22×#612711yescharacteristic
1129C22C22×#612711yescharacteristic
1130C22C22×#612911yescharacteristic
1131C22C2×#8825111yescharacteristic
1132C22C2×#41×D1311yescharacteristic
1133C22#1171964811yescharacteristic
1134C22C23×C22⋊D1311yescharacteristic
1135C4—22no—
1136C4—24no—
1137C4—22no—
1138C4—22no—
1139C4—42no—
1140C4—41no—
1141C4—262no—
1142C4—521no—
1143C4—522no—
1144C4—521no—
1145C4—521no—
1146C4—522no—
1147C4—521no—
1148C4—522no—
1149C4—521no—
1150C4—521no—
1151C4—522no—
1152C4#1171949614yes—
1153C4#1171951114yes—
1154C2—24no—
1155C2—44no—
1156C2—44no—
1157C2—522no—
1158C2C2×#1171949611yescharacteristic
1159C2C2×#1171926211yescharacteristic
1160C2#1312825811yescharacteristic
1161C2C2×#1171951111yescharacteristic
1162C2#41×C22⋊D1311yescharacteristic
1163C2#1312839411yescharacteristic
1164C2#1312844011yescharacteristic
subgroupG/H
centerC22×C4C23×D13
commutator, socle, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C4×D4×C13C2
prime radical#13118186C2
hypercenterC22×C4×D4D13
hypocenterC13#34700
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11719262C2semidirect
2. #13119076C2semidirect
3. #13118896C2semidirect
4. #13118737C2semidirect
5. #13118702C2semidirect
6. #13118617C2semidirect
7. #13118554C2semidirect
8. #13118483C2semidirect
9. #13118407C2semidirect
10. #13118322C2semidirect
11. #13118298C2semidirect
12. #13118281C2semidirect
14. #13118095C2semidirect
15. #13118078C2semidirect
16. C4×#88190C2semidirect
17. C4×#88178C2semidirect
18. C4×#88192C2semidirect
19. C4×#88207C2semidirect
20. #13117301C2semidirect
21. #13117219C2semidirect
22. C42×C22⋊D13C2semidirect
23. C22×C4×D4×C13C2semidirect
44. C2×C4×C22⋊D13C22semidirect
45. C2×C4×C22⋊D13C22semidirect
46. C2×#88180C22semidirect
47. C2×#88180C22semidirect
50. C2×#88151C22semidirect
51. C2×#88144C22semidirect
52. C2×#88137C22semidirect
53. C2×#88133C22semidirect
54. C2×C42×D13C22semidirect
55. C2×C4×Dic26C22semidirect
68. #11718874C22semidirect
69. #11718874C22semidirect
73. #11718873C22semidirect
74. #11718873C22semidirect
75. #11718872C22semidirect
76. #11718872C22semidirect
79. #11718871C22semidirect
80. #11718871C22semidirect
85. C4×C22⋊Dic13C22semidirect
86. C4×C22⋊Dic13C22semidirect
87. C4×C22⋊Dic13C22semidirect
88. C4×C22⋊Dic13C22semidirect
89. #11718655C22semidirect
90. #11718648C22semidirect
91. #11718647C22semidirect
92. #11718646C22semidirect
93. #11718646C22semidirect
94. #11718645C22semidirect
95. #11718644C22semidirect
96. #11718638C22semidirect
97. #11718635C22semidirect
98. #11718634C22semidirect
99. #11718622C22semidirect
100. #11718620C22semidirect
101. #11718617C22semidirect
102. #11718614C22semidirect
103. #11718613C22semidirect
104. #11718613C22semidirect
105. #11718613C22semidirect
106. #11718612C22semidirect
107. #11718612C22semidirect
108. #11718610C22semidirect
109. #11718609C22semidirect
110. #11718606C22semidirect
111. #11718606C22semidirect
112. #11718605C22semidirect
113. C4×#6103C22semidirect
114. C4×#6103C22semidirect
115. C4×#6103C22semidirect
116. C4×C4⋊Dic13C22semidirect
117. #11718594C22semidirect
118. C4×#6101C22semidirect
119. C4×#6101C22semidirect
120. C4×#6101C22semidirect
121. C4×#6101C22semidirect
122. C42×Dic13C22semidirect
123. #11718590C22semidirect
124. #11718589C22semidirect
155. C4×D4×C13D4semidirect
407. C22×C4×D4D13semidirect
662. C22×C13#529semidirect
742. C4×D4C22⋊D13semidirect
987. C13#34700semidirect
1127. C22#11719262semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117192622
#131190762
#131188962
#131187372
#131187022
#131186172
#131185542
#131184832
#131184072
#131183222
#131182982
#131182812
#131181862
#131180952
#131180782
C4×#881902
C4×#881782
C4×#881922
C4×#882072
#131173012
#131172192
C42×C22⋊D132
C22×C4×D4×C132
#3470013